Statistical ensemble models to forecast the Australian macadamia crop

Abstract

In this study, two levels of crop predictions were produced for the Australian macadamia industry for each of the six separate production regions. Firstly, the overall longer-term forecast was based on tree census data from growers in the Australian Macadamia Society (AMS), scaled up to include non-AMS orchards. Expected yields were based on historical data provided by the growers, with a nonlinear regression model incorporating the interacting effects of tree age, variety, year, region and tree spacing. Orchard decline amongst older trees, which has recently become more apparent, was also incorporated into the yield model. Long-term forecasts were made out to about 10 years, after which the effects of (unknown) future plantings, tree removals and rejuvenation of orchards begin to have a major impact.

The second level of crop prediction was an annual climate-based adjustment of these overall long-term estimates, taking into account the expected effects of the previous year’s climate on production. The dominant climatic variables were observed temperature, rainfall and solar radiation, and modelled water stress. Based on the proven forecasting success of boosted regression trees and ‘random forests’ statistical methods, the average forecast from an ensemble of general linear regression models was adopted (rather than using a single best-fit model). Exploratory multivariate analyses and nearest-neighbour methods were also used to investigate the annual patterns in the data. In parallel, AMS each year conducts an annual survey of about 20 key industry growers and consultants. Their replies were integrated into a ‘growers forecast’ for each year, and this is also taken into account when the AMS releases its annual crop forecast.